IE Courseware: Courses

Overview of optimization concepts: modeling-analysis-decision loop in financial and economic practice; linear, non-linear, integer and dynamic programming applications in finance and economics. Discrete optimization models in finance: modeling possibilities through binary and integer variables; relaxation methods; branch-and-bound methods; simulated annealing and genetic algorithms. Quadratic and convex programming, applications in portfolio management by using of linear and nonlinear programming software.

This course has two main parts.

First half covers numerical methods relevant to solving the partial differential equations, which arise in finance. Both the theoretical background and practical issues are treated. Topics include: background material in partial differential equations, examples of exact solutions including Black Scholes and its relatives, finite difference methods including algorithms and the connection with binomial models, interest rate models, early exercise, and the corresponding free boundary problems, and a brief introduction to additional difficulties of the multi-factor models.
Second half presents standard topics in simulation including random variable generation, variance reduction methods and statistical analysis of simulation output. The topics addressed include importance sampling, martingale control variables, stratification and the estimation of derivatives. Additional topics include the pricing of American options using Monte Carlo methods, pricing interest rate dependent claims, and the use of low discrepancy sequences.